The Morse index theorem for regular Lagrangian systems
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Submission date: 01. Jul. 2003
paper submitted to: Topology
MSC-Numbers: 34B05, 53C22, 58C50, 58E10, 70H05
Keywords and phrases: regular lagrangian system, index form, spectral flow, relative morse index, maslov index, maslov-type index
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In this paper, we prove the Morse index theorem for the index forms of regular Lagrangian systems with selfadjoint boundary condition coming from variational problems. We then give the relationship of them under two different boundary conditions. The Morse index theorem for the corresponding second order selfadjoint differential operators will be proved in recent paper: B. Booss and C. Zhu, The general spectral flow formula.